Astronomy Principles and Practice Fourth Edition.pdf

Interplanetary transfer orbits 201
Figure 14.12. Transfer and return from one orbit to another, illustrating the term ‘waiting time’.
Equation (14.14) may be used with equation (14.13) to compute the available epochs for the
return journey. The waiting time interval t W between the arrival time at C (figure 14.11) and the first
available departure time from P 2 can then be found and can be added on to 2τ to give the round trip
time or mission time t M . Thus,
t M = 2τ + t W . (14.15)
From symmetry considerations the minimum waiting time t W can be readily obtained. If P 1 is
β radians ‘ahead’ of P 2 when a transfer from P 1 to P 2 has just ended, as in figure 14.12(a), the first
available transfer back from P 2 to P 1 will begin when P 1 is β radians ‘behind’ P 2 .
Hence, if S is the synodic period of the two particles,
( ) 2π − 2β 2π − 2β
t W =
S = . (14.16)
2π n 1 − n 2
Alternatively, if P 1 were β radians ‘behind’ P 2 when an outward transfer (P 1 to P 2 )hasjust